What does the graph of $$y = \text{sqrt}(x)$$ look like?

The graph of $$y = \text{sqrt}(x)$$ starts at the origin (0,0) and increases gradually to the right.

What is the effect of changing the input of the square root function?

Changing the input affects the horizontal position of the graph. For example, $$y = \text{sqrt}(x - 4)$$ shifts the graph to the right by 4.

What is the parent function of the cube root?

The parent function is the cube root function, represented as $$y = \text{cbrt}(x)$$ .

What is the domain of the cube root function?

The domain is all real numbers, x ∈ ℝ.

What is the range of the cube root function?

The range is all real numbers, y ∈ ℝ.

How do you match an equation to its graph?

You analyze the transformations and shifts in the equation to determine how it modifies the parent function's graph.

What is the equation for a vertical shift of the cube root function?

A vertical shift can be represented as $$y = \text{cbrt}(x) + k$$ , where k is the shift amount.

What is the equation for a horizontal shift of the cube root function?

A horizontal shift can be represented as $$y = \text{cbrt}(x - h)$$ , where h is the shift amount.

What is the difference between square root and cube root functions?

Square root functions have a domain of x ≥ 0, while cube root functions have a domain of all real numbers.

HW 4.6 Square and Cube Root Graphs Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the parent function of the square root?

Back

2.

FLASHCARD QUESTION

Front

What is the equation for the cube root function?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

The domain is x ≥ 0.

5.

FLASHCARD QUESTION

Front

Back

The range is y ≥ 0.

6.

FLASHCARD QUESTION

Front

What is the effect of adding a constant to the square root function?

Back

7.

FLASHCARD QUESTION

Front

What is the effect of subtracting a constant from the square root function?

Back

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